First-half strikes from midfielders Tom Rogic and James Forrest had the Northern Irishman’s first piece of silverware since taking over the club in the summer all but guaranteed by the interval.

Striker Moussa Dembele confirmed that achievement when he scored from the penalty spot in the 63rd minute after Forrest was felled by Anthony O’Connor inside the box and the champions ran out convincing winners.

Afterwards, the Hoops boss spoke about the significance to a club that played its first game in 1888.

The former Swansea and Liverpool boss, who also played down the prospect of a domestic treble, saying: “I am thinking about Motherwell”, Celtic’s opponents next week, heaped praise on skipper Scot Brown, who has been rejuvenated this season.

Rodgers said: “I couldn’t be more proud for the team and if I am to say anything on getting my first trophy as Celtic manager, to have Scott as the captain is a huge honour.

“He is someone who represents how we work every day, his intensity, energy, enthusiasm. He wants to be the best and that is no different whether it is here or Alloa, he is up for every game.

“So again, outstanding control of the game, he dominated the game today and collectively he pulls the team together on the field and you see him improving tactically.

“(There were) So many outstanding performers, but he was certainly right up there.

“I am pleased with the performance. I thought tactically the team were excellent and we showed our quality when we got the ball.